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arXiv:2109.09732 · Physical review. B./Physical review. B

Dynamical signatures of thermal spin-charge deconfinement in the doped Ising model

Lauritz Hahn, Annabelle Bohrdt, Fabian Grusdt

Published Jun 27, 2022• 11 citations
arXivHTMLPDF

Abstract

The mechanism underlying charge transport in strongly correlated quantum systems, such as doped antiferromagnetic Mott insulators, remains poorly understood. Here, we study the expansion dynamics of an initially localized hole inside a two-dimensional (2D) Ising antiferromagnet at variable temperature. Using a combination of classical Monte Carlo and truncated-basis methods, we reveal two dynamically distinct regimes: a spin-charge confined region below a critical temperature ${T}^{*}$, characterized by slow spreading, and a spin-charge deconfined region above ${T}^{*}$, characterized by an unbounded diffusive expansion. The deconfinement temperature ${T}^{*}\ensuremath{\approx}0.65{J}_{z}$ we find is around the N\'eel temperature ${T}_{\mathrm{N}}=0.567{J}_{z}$ of the Ising background in 2D, but we expect ${T}^{*}<{T}_{\mathrm{N}}$ in higher dimensions. In both regimes we find that the mobile hole does not thermalize with the Ising spin background on the considered time scales, indicating weak effective coupling of spin and charge degrees of freedom. Our results can be qualitatively understood by an effective parton model and can be tested experimentally in state-of-the-art quantum gas microscopes.

DOI
10.1103/physrevb.105.l241113

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The mechanism underlying charge transport in strongly correlated quantum systems, such as doped antiferromagnetic Mott insulators, remains poorly understood. Here, we study the expansion dynamics of an initially localized hole inside a two-dimensional (2D) Ising antiferromagnet at variable temperature. Using a combination of classical Monte Carlo and truncated-basis methods, we reveal two dynamically distinct regimes: a spin-charge confined region below a critical temperature T∗{T}^{*}T∗, characterized by slow spreading, and a spin-charge deconfined region above T∗{T}^{*}T∗, characterized by an unbounded diffusive expansion. The deconfinement temperature T∗\ensuremath≈0.65Jz{T}^{*}\ensuremath{\approx}0.65{J}_{z}T∗\ensuremath≈0.65Jz​ we find is around the N'eel temperature TN=0.567Jz{T}_{\mathrm{N}}=0.567{J}_{z}TN​=0.567Jz​ of the Ising background in 2D, but we expect T∗<TN{T}^{*}<{T}_{\mathrm{N}}T∗<TN​ in higher dimensions. In both regimes we find that the mobile hole does not thermalize with the Ising spin background on the considered time scales, indicating weak effective coupling of spin and charge degrees of freedom. Our results can be qualitatively understood by an effective parton model and can be tested experimentally in state-of-the-art quantum gas microscopes.
The interplay of spin and charge degrees of freedom is believed to underlie various unresolved phenomena in strongly correlated systems. Quantum simulators based on neutral atoms provide an excellent testbed for investigating such phenomena and resolving their microscopic origins. Up to now, the majority of experimental and theoretical studies has focused on systems with fermionic exchange statistics. Here we expand the existing cold atom toolbox through the use of negative temperature states, enabling us to realize an antiferromagnetic, bosonic t−Jt-Jt−J model in two spatial dimensions, subject to a strong staggered magnetic field in a quantum gas microscope. Through comparison of the spreading dynamics of a single hole in a Néel versus a spin-polarized initial state, we establish the relevance of memory effects resulting from the buildup of strong spin-charge correlations in the dynamics of charge carriers in antiferromagnets. We further numerically predict rich dynamics of pairs of doped holes, which we demonstrate to be bound by a similar memory effect, while their center-of-mass can expand freely. Our work paves the way for the systematic exploration of the effect of antiferromagnetic spin ordering on the properties of individual charge carriers as well as finite doping phases: Our study demonstrates that the staggered field can be used to single out the effect of antiferromagnetism and holds the prospect to prepare low-temperature states in the near future.
Abstract Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t–J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number z ̃ = 4 . Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.
Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases.We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy J. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.
Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy JJJ. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.
The interplay of spin and charge degrees of freedom is believed to underlie various unresolved phenomena in strongly correlated systems.Quantum simulators based on neutral atoms provide an excellent testbed for investigating such phenomena and resolving their microscopic origins.Up to now, the majority of experimental and theoretical studies has focused on systems with fermionic exchange statistics.Here we expand the existing cold atom toolbox through the use of negative temperature states, enabling us to realize an antiferromagnetic, bosonic t -J model in two spatial dimensions, subject to a strong staggered magnetic field in a quantum gas microscope.Through comparison of the spreading dynamics of a single hole in a Néel versus a spin-polarized initial state, we establish the relevance of memory effects resulting from the buildup of strong spin-charge correlations in the dynamics of charge carriers in antiferromagnets.We further numerically predict rich dynamics of pairs of doped holes, which we demonstrate to be bound by a similar memory effect, while their center-of-mass can expand freely.Our work paves the way for the systematic exploration of the effect of antiferromagnetic spin ordering on the properties of individual charge carriers as well as finite doping phases: Our study demonstrates that the staggered field can be used to single out the effect of antiferromagnetism and holds the prospect to prepare low-temperature states in the near future.
We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t-J_{z} model can be understood in terms of spinless chargons coupled to a Z_{2} lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z_{2} electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J_{z}, i.e., well within reach of current experiments.